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I recently received a comment on this blog proposing that believing in a creator is a logical choice, because the likelihood that we’re living in a simulation that isn’t simulated by someone else is vanishingly small. I thought it was an interesting remark at the time, though I didn’t agree with it.

Then, just a few days later, I heard the same argument again, this time from my friend Dan Miller, who’s an occasional contributor to this blog. It turns out that this meme apparently originates with a fellow called Nick Bostrom, who framed the argument in a paper in 2003.

However, when Bostrom framed it, the proposal was presented as one of a set of fairly reasonable options. It seems to me that he was quoted somewhat out of context. The public have grabbed a nice-looking Matrix-y idea and run with it. I’d like to take a look at this argument in it’s popular form and point out why, IMO, it’s badly flawed.

First, though, for all those people who don’t follow every single comment on my blog, which I assume is everyone except me, let’s at least do justice to the original proposal that’s out there in meme-land. We might frame it as follows:

We can already simulate universes much simpler than our own.

We aspire to simulate entities such as ourselves through natural curiosity.

It’s reasonable to presume that other intelligent entities would behave similarly.

Given this, the probability that we ourselves are being simulated his high.

It sounds nice, so long as you don’t look too closely, and provides a cozy rationalization for believing in something vaguely god-like. However, the main problem I see goes like this:

If we’re probably being simulated, so, by extrapolation, are those above us doing the simulating.

Given that we have no idea what the maximum possible computational universe of a universe larger than ours is, we are forced to conceive of an infinite stack of simulations.

Given such a stack, we must also presume that intelligent beings become less likely to tinker with their creations once they’ve built them. In other words, the smarter you are and the more creative power you have, the less likely you are to exercise an act of will. Otherwise, we should expect someone up there in the infinite stack to be constantly fiddling with the rules, or turning the stack below them off and rebooting at every moment.

If we propose decreasing proactive behavior for each level, we have to ask how come the simulation stack was created in the first place. However, if we don’t, we have to throw away the notion that the universe follows orderly laws. In other words, we have to throw away science.

Note that in this argument, we haven’t even started to consider the fact that more and more complex universes entail more and more complex rules on which they run. And this, of course, falls foul of the principle of descriptive minimalism that I’ve discussed in previous posts. More complex universes are far less likely to be the one that we’re in. The more a universe is simulatable, the less likely it is that it exists as a nested subset.

Hence, to my mind, the whole idea of digital physics is a refutation of the simulation hypothesis. We argue that the universe is finite precisely because it does away with excess, non-provable twaddle, like many of the properties of real numbers.

I’m not really familiar with Bostrom’s work, so I’m going to have to go back and have a closer look at it. However, his original remarks appear to be very carefully worded. Of the options he outlines, it seems to me that there is ample evidence to believe in number one:

The fraction of human-level civilizations that reach a posthuman stage is very close to zero